OpenEuphoria

Re: [OT] How many integers?

• Posted by Igor Kachan <kinz at peterlink.ru> Jun 09, 2003
• 348 views

Hello Matt:

> 
> rforno at tutopia.com wrote:
> > You know, the set of *all* integers (abstract integers, not
> > Euphoria nor C nor computer integers) is infinite, but larger than
> > the set of *even* integers, that is also infinite.
> 
> Actually, the set of even integers (let's call it ZE) and the set of all 
> integers (Z) are the same size (countably infinite).  The standard way 
> to prove this is to use some function to map from one set to the other, 
> showing that there is the sets map each other completely with a 
> one-to-one relationship  (bijective):
> 
> Then for any z in Z, there is a ze in ZE such that z = ze / 2.  In other 
> words, for any normal integer, I can use even integers to 'count' the 
> normal integers, and so the sets must be the same size (btw, the set of 
> rational numbers is the same size, but any interval of real numbers will 
> be bigger).
> 
> Matt Lewis

I say, Russian is better for such the things  
We say "power of a set", not "size of a set".
 
Regards,
Igor Kachan
kinz at peterlink.ru